Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{9y^2 - 12y + 4 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-12)^2 - 4.9.4}[/tex]
[tex]\mathsf{\Delta = 144 - 144}[/tex]
[tex]\mathsf{\Delta = 0}[/tex]
[tex]\mathsf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{12 \pm \sqrt{0}}{18} \rightarrow \begin{cases}\mathsf{y' = \dfrac{12 + 0}{18} = \dfrac{12}{18} = \dfrac{2}{3}}\\\\\mathsf{y'' = \dfrac{12 - 0}{18} = \dfrac{12}{18} = \dfrac{2}{3}}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \left\{\dfrac{2}{3}\right\}}}}[/tex]
[tex]\mathsf{x^2 - 3 = 4x + 2}[/tex]
[tex]\mathsf{x^2 - 4x - 5 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-4)^2 - 4.1.(-5)}[/tex]
[tex]\mathsf{\Delta = 16 + 20}[/tex]
[tex]\mathsf{\Delta = 36}[/tex]
[tex]\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{4 \pm \sqrt{36}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{4 + 6}{2} = \dfrac{10}{2} = 5}\\\\\mathsf{x'' = \dfrac{4 - 6}{2} = -\dfrac{2}{2} = -1}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \left\{5;-1\right\}}}}[/tex]
[tex]\mathsf{-x^2 - x + 30 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-1)^2 - 4.(-1).30}[/tex]
[tex]\mathsf{\Delta = 1 + 120}[/tex]
[tex]\mathsf{\Delta = 121}[/tex]
[tex]\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{121}}{-2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{1 + 11}{-2} = -\dfrac{12}{2} = -6}\\\\\mathsf{x'' = \dfrac{1 - 11}{-2} = \dfrac{-10}{-2} = 5}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \left\{5;-6\right\}}}}[/tex]
[tex]\mathsf{(x - 5)^2 = 1}[/tex]
[tex]\mathsf{x^2 - 10x + 25 = 1}[/tex]
[tex]\mathsf{x^2 - 10x + 24 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-10)^2 - 4.1.24}[/tex]
[tex]\mathsf{\Delta =100 - 96}[/tex]
[tex]\mathsf{\Delta =4}[/tex]
[tex]\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{10 \pm \sqrt{4}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{10 + 2}{2} = \dfrac{12}{2} = 6}\\\\\mathsf{x'' = \dfrac{10 - 2}{2} = \dfrac{8}{2} = 4}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \left\{6;4\right\}}}}[/tex]
[tex]\mathsf{3x^2 + 55 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (0)^2 - 4.3.55}[/tex]
[tex]\mathsf{\Delta = 0 - 660}[/tex]
[tex]\mathsf{\Delta = -660}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \left\{\emptyset\right\}}}}[/tex]
[tex]\mathsf{x^2 - 6x = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-6)^2 - 4.1.0}[/tex]
[tex]\mathsf{\Delta = 36 - 0}[/tex]
[tex]\mathsf{\Delta = 36}[/tex]
[tex]\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{6 \pm \sqrt{36}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{6 + 6}{2} = \dfrac{12}{2} = 6}\\\\\mathsf{x'' = \dfrac{6 - 6}{2} = \dfrac{0}{2} = 0}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \left\{6;0\right\}}}}[/tex]
